A Finite Multiplicity Helson-Lowdenslager-De Branges Theorem

Details A Finite Multiplicity Helson-Lowdenslager-De Branges Theorem A Finite Multiplicity Helson-Lowdenslager-De Branges Theorem

2009-10-28

arxiv.org/abs/0910.5416v1

Mathematics

Functional Analysis

18 pages

Scientific paper

This paper proves two theorems. The first of these simplifies and lends clarity to the previous characterizations of the invariant subspaces of $S$, the operator of multiplication by the coordinate function $z$, on $L^2(\mathbb{T};\mathbb{C}^n)$, where $\mathbb{T}$ is the unit circle, by characterizing the invariant subspaces of $S^n$ on scalar valued $L^p$ ($0

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